How to create this type of gradient background lighting?
To do this you can use a textured emission plane (you could simulate it with an out of focus mesh lamp too, but a plane will be less noisy).


Add a big plane behind your scene:


Give it a procedural gradient material:



The Object coordinates are centered around the object's Origin, so by default that's where the gradient will be centered.

To adjust the size and scale of the gradient, you can tweak the settings on the Mapping node

I've also made the plane brighter than it appears to the camera by using different emission shaders based on the Camera Ray output of the Light Path node, to avoid over exposing the background a lot.
Render




This way glossy floor plane will reflect the light from the plane, creating a neat effect.